Finite-temperature entanglement negativity of free fermions

Hassan Shapourian, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper (Shapourian et al 2017 Phys. Rev. B 95 165101). In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.

Original languageEnglish (US)
Article number43106
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
StatePublished - Apr 30 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Conformal field theory
  • Entanglement entropies
  • Entanglement in extended quantum systems


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